Mathematics - Circle Question with Solution | TestHub

Equation of pair of tangents is given by ${\mathrm{SS}}_1={\mathrm{T}}^2$ $$\begin{array}{l}\text{ or }\mathrm{S}={\mathrm{x}}^2+{\mathrm{y}}^2+20(\mathrm{x}+\mathrm{y})+20,{\mathrm{S}}_1=20\\ \mathrm{T}=10(\mathrm{x}+\mathrm{y})+20=0\\ \therefore {\mathrm{SS}}_1={\mathrm{T}}^2\\ \Rightarrow 20\left({\mathrm{x}}^2+{\mathrm{y}}^2+20(\mathrm{x}+\mathrm{y})+20\right)=10^2\\ (\mathrm{x}+\mathrm{y}+2{)}^2\\ \Rightarrow 4{\mathrm{x}}^2+4{\mathrm{y}}^2+10\mathrm{xy}=0\Rightarrow 2{\mathrm{x}}^2+2{\mathrm{y}}^2+5\mathrm{xy}=0\end{array}$$